Golden Ratio

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Transcript of Golden Ratio

By Rosie Cui The Golden Ratio The Golden ratio is considered a special number, which is equal to 1.61803398875. The golden ratio is also known as divine proportion, golden section and golden mean, The symbol that represents the Golden Ratio is phi which looks like a circle with an I through the centre of the circle vertically. If you find the ratio of a certain shape by dividing the length by the width of that shape and the ratio is equivalent to the golden ratio that shape is considered most pleasing to the eye. The Golden Ratio The dimensions of the Great Pyramid are somewhat debatable because the limestone casing no longer exists and some of the surface has eroded during the years. The sloping height of the great pyramid divided by half the base length of one side equals the golden ratio by three decimal places. This makes the pyramid appealing to the eye. The base of the pyramid is 755.8 cubits and half of that being 377.9 cubits. When you divide the sloping height of 612 cubits by the half the base length of 377.9the result is 1.619, almost0 the Golden ratio. The Golden Ratio in The Great Pyramid The Fibonacci spiral and the golden rectangle is often found in appealing photos. The human eye is often attracted to things with divine proportion such as the photos below. The Fibonacci spiral, Golden rectangle and golden ratio is often found in nature and some photographers often try to put these into their photographs making them more appealing. It is said that if the shape follows the line of the Fibonacci spiral it appeals to the eye. The Golden Ratio in Photography Many people find this rectangle more appealing to other rectangles because it has the ratio of 1:1.61803398875 and the other rectangles don't.The Golden rectangle reflects the Fibonacci sequence as shown below because you start with a rectangle with an area of 1 and then beside it another one with an area of one and then 2 and then 3 and then 5 and so on.

The Fibonacci Sequence0,1,1,2,3,5,8,13,21 ....This work because the 3rd number ( 1) is the sum of the 2 previous numbers (0, 1). (0+1 =1). this continues throughout the sequence and it never ends. The Golden Rectangle In CubitsSloping height / (1/2 of side length)612.01 / (1/2 of (x)755.8)612.01 / 377.9= 1.61950251389

This means that 1.61950251389 is 0.00146852514 off the Golden ratio Working Out The Golden Ratio in the Great Pyramid The Pythagoras Theorem helps find the Golden Ratio in the Great Pyramid because if you know the base length and the perpendicular height you can find the sloping height which will help you find the Golden ratio. If you have a right angled triangle and you know the base length (b) and the height (a) you can find out the sloping height (c)by drawing a square on each of the sides you will find that the area of a2+b2=c2. This applies to the Great Pyramid because in the Great Pyramid the right angled triangle (as pictured in the last slide) a2+b2=c2(481.4x 481.4)+(377.9x 377.9)=231745.96 + 142808.41= 374554.37Sloping height equals square root of 374554.37=612.008472164 Pythagoras Theorem I think that that the Egyptians knew about the Golden Ratio when they built the Pyramids.I believe this because the pyramids almost have the exact value of the golden ratio in the pyramid, the base is nearly perfectly shaped and the angles are all about the sames. This leads me to believe that they were great mathematicians at the time so they knew about this golden ratio and followed this to create the pyramids. I do not believe that aliens could have come to Egypt to build the pyramids just for the Pharaoh. I highly doubt this theory because there would have been evidence and why didn't they build something magnificent when our royals died? This leads me to my conclusion which I believe that because of the pyramids accuracy and the small evidence found about how they built the pyramids the Egyptians knew about the Golden ratio and many other mathematical theories (including the Pythagoras theorem) when they built the pyramids. Evaluation The Fibonacci Sequence0,1,1,2,3,5,8,13,21 ....This work because the 3rd number ( 1) is the sum of the 2 previous numbers (0, 1). (0+1 =1). this continues throughout the sequence and it never ends.The Fibonacci spiral connects the rectangles together in the golden rectangle to make a special spiral that is often found in nature, photography and is appealing to the eye.

This relates to the Golden ration because when you divide a number by the one before it the answer is very close to the golden ratio but it never is exactly.eg.13/8=1.625 Fibonacci Spiral BY ROSIE CUI THANK YOU !